By “Brexit times five”, Trump is referring to the surprising referendum result in favour of Britain leaving the European Union, an outcome that went against the predictions of most polls. Given the unexpected triumph of Britain’s “Leave” campaign, is it possible that Trump could produce a surprise result of even greater proportions?

Many explanations are put forward to account for voting patterns, especially when they don’t match the polls.

Good sampling methodology – that is, how to choose a group of people likely to reflect the characteristics of the broader population – is key to ensuring accurate and useful results. An understanding of likely voter turnout is also important, especially in the US and other countries where voting is voluntary.

But other factors, such as the language and wording used, can also effect the results of any survey, including electoral polls.

One likely factor in the discrepancy between the pre-referendum Brexit polls and the final result was social desirability bias – the human tendency to portray ourselves in the most favourable light. This bias may not necessarily be conscious. It’s common in social surveys, where the need to be seen to be doing “the right thing” can overwhelm honest responses.

For example, it’s socially desirable for people to disagree with the statement “I sometimes feel resentful when I don’t get my own way”, even though it’s likely everybody has felt this way at some time. Self-reporting of alcohol consumption is typically 40-50% lower than actual consumption rates.
In the case of Brexit, the “Leave” campaign became associated with xenophobia and racism. Because this was regarded negatively by mainstream society, it likely resulted in people understating their support for the “Leave” campaign when asked by pollsters.

Social desirability bias is exacerbated by the presence of other people, so it’s more prominent when survey questions are asked directly by an interviewer, either in person or over the phone.

If social desirability was a factor in the inconsistency between the Brexit polls and the final result, we should see a difference between the polls taken by telephone interviews and those conducted online.
Let’s look at the polls from the final week of the Brexit campaign. Out of five telephone polls, none predicted a win for “Leave”. Out of eight online polls, four predicted a win.

This is particularly surprising because one might expect lower polling for the “Leave” vote in online polls, since this method captures younger voters who were (at least publically) more opposed to Brexit. Assuming no other methodological issues were at play, this suggests that social desirability may have been a factor.

Like the “Leave” campaign, Trump’s campaign is associated with the socially negative attributes of xenophobia and racism, as well as sexism and allegations of sexual misconduct. This is likely to cause a social desirability bias with a tendency for people to under report their support for Trump.

Now let’s look at Trump’s “Brexit times five” claim. In both telephone and online polls taken during the last week of the Brexit campaign, the average result was 46.5% for “Remain” and 44.5% for “Leave”. Excluding the undecided voters, this equates to 51% for “Remain” and 49% for “Leave”.
The result of the actual vote was 48% for “Remain” and 52% for “Leave”. On the basis of this simplistic analysis, and with this particular mix of telephone and online polls, we could argue that social desirability bias suppressed the polled support for “Leave” by around 3%.

As of November 1, the US polling aggregation website FiveThirtyEight says the national averages for the popular vote in the US election are 49.2% for Clinton and 44.5% for Trump, a difference of 4.7% in favour of Clinton.

If Trump is able to achieve “Brexit times five” – that is, gain 15% more votes on election day than the polls would suggest – he would indeed be well-placed for victory. But unlike Brexit, this result would need to be repeated in each state and reflected in the Electoral College votes, rather than just a single national vote.

Although important and often present, the effects of social desirability bias are likely to be relatively minor in polls that are properly conducted, and only likely to cause surprise results in a tight race. The degree to which the polling averages may be misled by social desirability bias depends on the mix of methods used to collect the answers – with a greater reliance on telephone polling more likely to capture a greater degree of bias.

So while it’s possible that Trump’s polling is depressed, and while he may win more votes than expected on Election Day, he’s still unlikely to win the Presidency.

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